The physical basis for having recombinant offspring is the the physical crossing over events-- the chiasmata --which form in meiosis I. Homologous chromosomes paired in prophase I come apart at matching points and reattach to each other (hence "crossing" over, which in this case is literal).
Work Step by Step
Review Ch. 13 and see the physical exchange of DNA between non-sister chromatids. This is illustrated several times in the chapter.